Motivated by prior work [1]}, [2]}, [3]}, [4]}, we propose a nonlocal patch-based regularizer for multiband remote sensing images.
Unlike VTV [5]}, where variations along just horizontal and vertical directions are penalized, we use a wider search window both in terms of nonlocality and directionality.
Another novelty of our proposal is the use of patches for computing weights which are used in the regularizer. While the idea of weighting is not exactly new, the distinction is precisely in how the weighting is performed. For example, in [2]}, [3]} the weights are derived from the reconstruction and this makes the regularizer and the overall optimization nonconvex. Indeed, unlike image denoising [8]}, a good surrogate of the ground-truth is not available for problems such as deblurring and inpainting and coupling the weight computation with the reconstruction seems to be a natural option.
However, for the fusion problem at hand, we have a high resolution image \(\mathbf {Y}_h\)  of the same scene as the reconstruction and we use this
